It's the same reason the fly in your car is just buzzing around in the same place near your face even though the car is going 80 mph on the freeway. But let's start back at the beginning.
So you hop into your Lamborghini, fasten you seat belt, and reach over to start that 800 HP V10. As you do you notice a fly sitting on the steering wheel. No big deal; so you start your behemoth. And accelerate 0 to 80 in 2.5 seconds.
The fly is still there on the steering wheel. So you, the car, and the fly are doing 80 mph together. This is important, you and the fly are both doing 80 mph now.
Now the fly, bored a bit, springs straight up from the steering wheel and hovers there in front of your face. But you, the car, and the fly are still going 80 mph down the freeway. The fly sprang straight upward to hover, it did nothing fore and aft in the direction of the car to slow or speed it up...relative to the car.
And like that fly, that's why a helo just hovers above the ground it rose from.
Like the fly on the steering wheel is going 80 mph with the 80 mph car speed, the helo on the ground is going 1000 mph with the 1000 mph rotation of the planet.
This is important...because the planet is rotating at 1000 mph and the helo is just riding along on the ground, it's also going 1000 mph like that fly that was also going 80 mph with the car. And when the helo and the planet are both going the same speed in the same direction they are going zero mph relative to each other.
So now the helo pilot moves the collective and the helo lifts directly up, vertical from the ground. Because it goes vertical relative to the ground, that does not add or subtract speed from that 1000 mph it was going when on the ground. So it's still going 1000 mph.
Because the planet is rotating at 1000 mph and the helo is still hovering at 1000 mph in the same direction as the rotation, the relative velocity between the helo and the Earth remains at zero mph.
And that is in essence why the helo stays directly above its launch site when it hovers.
NOTE: It's a bit more complex then that, but that is the basic idea.